Question

Name four values of b which make the expression factorable: x^2 - 3x + b

Answer 1

Answer:

2, -4, -10 and -18.

Step-by-step explanation:

The given expression is

$x^2-3x+b$      ...(i)

We need to find the 4 values of b which make the expression factorable.

A polynomial is factorable if both roots are real.

If $\alpha \text{ and }\beta$ are two real roots of a polynomial, then the polynomial is defined as

$P(x)=x^2-(\alpha+\beta)x+\alpha\beta$         ....(ii)

From (i) and (ii), we get

$\alpha+\beta=3$     ...(iii)

$\alpha\beta=b$

For equation (iii), possible pairs of $\alpha \text{ and }\beta$ are (2,1), (4,-1), (5,-2) and (6,-3).

From these ordered pairs the values of b are

$b=\alpha\beta=2\times 1=2$

$b=\alpha\beta=4\times (-1)=-4$

$b=\alpha\beta=5\times (-2)=-10$

$b=\alpha\beta=6\times (-3)=-18$

Therefore, the four possible values of b are 2, -4, -10 and -18.

Answer 2

Four values that make the expression factorable will be, 2, -4, -18 and -28.